Germany had never lost to their rivals by three or more goals but Ronald Koeman's side enjoyed a famous success in Amsterdam as Virgil van Dijk's first-half header was added to by late strikes from Memphis Depay and Georginio Wijnaldum.
Having failed to score in two of their three games when they crashed out of the World Cup group stage in June, Joachim Low's men are yet to score in either of their Nations League games after drawing 0-0 with France in their opening fixture.
They had multiple opportunities to end the drought in Amsterdam, with Werner wasting a first-half one-on-one and substitute Leroy Sane somehow steering an even better opening wide after the break, and their lack of goals is becoming a concern.
"We played very well at the beginning, created many chances, let them run without the ball and did everything we wanted to," Werner said in quotes published on UEFA's website.
"Then there is this corner which hits the bar and is then turned in [by Van Dijk]. That was a punch in our stomach. We missed out on scoring when we had the chances to do so. That's our biggest shortcoming."
Low admits his side's inability to score is perplexing to him.
"It's not only about converting the chances," he added.
"We played okay until we conceded and did not use our chances. After conceding, you could see that recent results have led to a lack of confidence.
"Why are we not scoring? That's difficult to answer, we have clear chances.
"Had we lost 1-0, it would have been acceptable, but breaking apart like this in the last 10 minutes is not good."
UEFA Nations League (@UEFAEURO) October 13, 2018
Mats Hummels, who also came close with a second-half header that Ryan Babel cleared, could not fathom how Germany had failed to find the net.
"It's a matter of converting chances, no doubt," he said.
"We lost 3-0 in a match we have to win, that's my opinion. It's not like one player is squandering all the chances, sometimes it's bad luck, sometimes ineptitude, my header is being cleared off the line.
"We play away in Holland, should have scored three or four, and lose 3-0."